I was trying to dig up something about deleted content from Skyrim, haven't found anything, but I've heard about old Civil War System.
Could someone explain with details what were those little things that were removed?

If the Stormcloaks took Markarth, Galmar himself would have executed Ondelemar.

http://uesp.net/wiki/Skyrim:Unfinished_Quests
http://uesp.net/wiki/Skyrim:Unused_NPCs

Those pages list the unifnished quests and NPCs - the majority of the cut content, I believe.
Also, if you're on PC, there are a number of mods which restore cut content.

-Sieges on both Riften or Markarth

-Dynamic fighting over forts

-If the civil war maps are any indications, settlements like Shor's Stone and Riverwood would be subject to capture

Unfortunately, they let their marketing hype set the release date.

there's an unused arena called the pit iirc

Yeah that was planed for Dark Brotherhood questline, but canceled.

And they planed to add that forts could be under attack, and if you don't go to defend them you lose them and have to re-counquer them.

Never let hype get the better of you, people. Always act like you've seen it all.

I suspected as much with the many forts scattered everywhere. It's a shame they rushed for a fancy release date...i say 12/12/12 is just as fancy and it would've been well worth the wait

Agreed, and we would certainly have more, and cooler contet and stuff. A lot was planned to implement even in DLCs, remeber Game Jam, what they did in only one week, if they didn't abandon Skyrim, imagine what we could have now.

Are we talking about the arena pit that was planned in Windhelm for gladatorial combat? That wasn't a Dark Brotherhood thing, they wanted to bring back arena stuff.

Not that it would've made sense in the final product. The Nords are stupid and honor-bound, but they don't seem to the type so foolish to kill for sport.

Honor before reason, indeed.